Hall calls have been assigned to a group of elevator cars by a large number of different strategies. A common strategy estimates the time of arrival (ETA) of each elevator car for a specific hall call to be assigned. A count is computed for each car which represents the time estimated for the car in question to reach the call floor with the proper service direction to serve the hall call. The hall call assignment is given to the car having the lowest ETA count. The call assignments are continuously reevaluated. When a previously assigned hall call is being reconsidered, reassignment to another car having a lower ETA than the presently assigned car is only made when the lower ETA is lower by T seconds. The constant T is preselected at the time the elevator system is installed. Indiscriminate switching of hall call assignments can result in so called "no-call stops", with the value for T being selected to minimize such stops, as they are non-productive, time consuming, and energy wasting.